Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math

def checkTriangular(n):
    odd = 1+(8*n)
    oddsqrt = math.sqrt(odd)
    return oddsqrt==int(oddsqrt)

num = int(input())
bool = False
diff = 1
i = 1
while i<=num//2:
	if checkTriangular(i) and checkTriangular(num-i):
		bool = True
		print('YES')
		break 
	diff += 1
	i += diff 
if bool==False:
    print('NO')